Explain why electrons in an atom can only occupy discrete energy levels rather than a continuous range of energies, and outline one piece of experimental evidence that supports this conclusion.

IB DP Physics Higher Level (2023 syllabus) — E.1 Structure of the atom · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Model answer (4 marks)

Electrons in atoms occupy stationary states in which they do not radiate energy. Only specific electron energies are allowed because the electron’s de Broglie wavelength must form a standing wave that fits exactly around the orbit, giving the quantisation condition nλ=2πr (or equivalently L=nħ). Consequently the electron can only exist in discrete energy levels.

Experimental evidence: the discrete line spectra of elements. When an atom emits or absorbs light, photons are produced only at specific frequencies. Each spectral line corresponds to a photon of energy E=hf that is emitted or absorbed when an electron jumps between two particular energy levels. The existence of these discrete lines therefore confirms that the energy levels themselves are discrete.

Examiner tips

  • Use the term ‘stationary states’ and ‘standing wave’ to show understanding of quantisation.
  • Mention the de Broglie condition or angular‑momentum quantisation explicitly.
  • Identify a discrete spectral line as evidence and link it to energy level transitions.
  • Keep the answer concise – 4 marks can be achieved with two short points.

Mark scheme (4 marks)

  1. Electrons in atoms exist in stationary states (allowed orbits/energy levels) in which they do not radiate energy.
  2. Only specific values of electron energy are permitted because the de Broglie wavelength of the electron must form a standing wave that fits exactly around the orbit (i.e. the angular momentum is quantised / nλ = 2πr).
  3. Identification of a valid experimental evidence: discrete line (emission or absorption) spectra of elements show that photons of only specific frequencies/energies are emitted or absorbed.
  4. Explicit link between evidence and discrete levels: each spectral line corresponds to a photon of energy E = hf emitted (or absorbed) when an electron transitions between two specific energy levels, so the existence of discrete lines confirms the energy levels themselves are discrete.

Key terms in this question

discrete energy levels

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